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- Seleznjev, Oleg, et al.
(författare)
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Run-length compression of quantized Gaussian stationary signals
- 2012
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Ingår i: Random Operators and Stochastic Equations. - : Walter de Gruyter GmbH. - 0926-6364 .- 1569-397X. ; 20:4, s. 311-328
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Tidskriftsartikel (refereegranskat)abstract
- We consider quantization of random continuous-valued signals. In practice, analogue signals are quantized at sampling points with further compression. We study probabilistic models for run-length encoding (RLE) algorithm applied to quantized sampled random signals (Gaussian processes). This compression technique is widely used in digital signal and image processing. The mean (inverse) RLE compression ratio (or data rate savings) and its statistical inference are considered. In particular, the asymptotic normality for some estimators of this characteristic is shown. Numerical experiments for synthetic and real data are presented.
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- Seleznjev, Oleg, et al.
(författare)
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Uniform and non-uniform quantization of Gaussian processes
- 2012
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Ingår i: Mathematical Communications. - : University of Osijek. - 1331-0623 .- 1848-8013. ; 17:2, s. 447-460
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Tidskriftsartikel (refereegranskat)abstract
- Quantization of a continuous-value signal into a discrete form (or discretization of amplitude) is a standard task in all analog/digital devices. We consider quantization of a signal (or random process) in a probabilistic framework. The quantization method presented in this paper can be applied to signal coding and storage capacity problems. In order to demonstrate a general approach, both uniform and non-uniform quantization of a Gaussian process are studied in more detail and compared with a conventional piecewise constant approximation. We investigate asymptotic properties of some accuracy characteristics, such as a random quantization rate, in terms of the correlation structure of the original random process when quantization cellwidth tends to zero. Some examples and numerical experiments are presented.
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- Shykula, Mykola, 1978-
(författare)
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Asymptotic quantization errors for unbounded quantizers
- 2007
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Ingår i: Theory of Probability and Mathematical Statistics. - : American Mathematical Society (AMS). - 0094-9000 .- 1547-7363. ; 75, s. 189-199
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Tidskriftsartikel (refereegranskat)abstract
- We consider non-uniform scalar quantization for a wide class of unbounded random variables (or values of a random process sampled in time). Asymptotic stochastic structures for quantization errors are derived for two types of quantizers when the number of quantization levels tends to infinity. The corresponding results for bounded random variables are generalized. Some numerical examples illustrate the rate of convergence.
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- Shykula, Mykola, 1978-
(författare)
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Quantization of Random Processes and Related Statistical Problems
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we study a scalar uniform and non-uniform quantization of random processes (or signals) in average case setting. Quantization (or discretization) of a signal is a standard task in all nalog/digital devices (e.g., digital recorders, remote sensors etc.). We evaluate the necessary memory capacity (or quantization rate) needed for quantized process realizations by exploiting the correlation structure of the model random process. The thesis consists of an introductory survey of the subject and related theory followed by four included papers (A-D).In Paper A we develop a quantization coding method when quantization levels crossings by a process realization are used for its coding. Asymptotical behavior of mean quantization rate is investigated in terms of the correlation structure of the original process. For uniform and non-uniform quantization, we assume that the quantization cellwidth tends to zero and the number of quantization levels tends to infinity, respectively.In Papers B and C we focus on an additive noise model for a quantized random process. Stochastic structures of asymptotic quantization errors are derived for some bounded and unbounded non-uniform quantizers when the number of quantization levels tends to infinity. The obtained results can be applied, for instance, to some optimization design problems for quantization levels.Random signals are quantized at sampling points with further compression. In Paper D the concern is statistical inference for run-length encoding (RLE) method, one of the compression techniques, applied to quantized stationary Gaussian sequences. This compression method is widely used, for instance, in digital signal and image processing. First, we deal with mean RLE quantization rates for various probabilistic models. For a time series with unknown stochastic structure, we investigate asymptotic properties (e.g., asymptotic normality) of two estimates for the mean RLE quantization rate based on an observed sample when the sample size tends to infinity.These results can be used in communication theory, signal processing, coding, and compression applications. Some examples and numerical experiments demonstrating applications of the obtained results for synthetic and real data are presented.
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- Shykula, Mykola, et al.
(författare)
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Stochastic structure of asymptotic quantization errors
- 2006
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Ingår i: Statistics and Probability Letters. - : Elsevier. - 0167-7152 .- 1879-2103. ; 76:5, s. 453-464
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Tidskriftsartikel (refereegranskat)abstract
- We consider quantization of continuous-valued random variables and processes in a probabilistic framework. Stochastic structure for non-uniform quantization errors is studied for a wide class of random variables. Asymptotic properties of the additive quantization noise model for a random process are derived for uniform and non-uniform quantizers. Some examples and numerical experiments demonstrating the rate of convergence in the obtained asymptotic results are presented.
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